Question 1180900
Here's how to analyze the motorcycle helmet use data:

**a. Probability of DOT-compliant helmet use:**

1. **Total observations:** Add up all the observations from each region: 1162 + 944 + 1092 + 1048 = 4246

2. **Total DOT-compliant helmets:** Add up the number of DOT-compliant helmets in each region: 928 + 798 + 873 + 848 = 3447

3. **Probability:** Divide the number of DOT-compliant helmets by the total number of observations: 3447 / 4246 ≈ 0.8118

**Therefore, the probability that a motorcyclist wears a DOT-compliant helmet is approximately 0.8118.**

**b. NHTSA's reaction:**

* The current probability of DOT-compliant helmet use is 0.8118.
* Five years ago, it was 0.48.
* Last year, it was 0.63.

The NHTSA would likely be *very* pleased with the most recent results.  The probability has increased significantly from both five years ago and last year. This suggests that their efforts to promote helmet use are potentially having a positive impact.

**c. Probability of DOT-compliant helmet use by region:**

To calculate the probability for each region, divide the number of DOT-compliant helmets in that region by the total number of observations in that region:

* **Northeast:** 928 / 1162 ≈ 0.7986
* **Midwest:** 798 / 944 ≈ 0.8453
* **South:** 873 / 1092 ≈ 0.8000
* **West:** 848 / 1048 ≈ 0.8092

**Here's a summary table:**

| Region    | DOT-Compliant Helmets | Total Observations | Probability |
| --------- | -------------------- | ------------------ | ----------- |
| Northeast | 928                 | 1162               | 0.7986      |
| Midwest   | 798                 | 944                | 0.8453      |
| South     | 873                 | 1092               | 0.8000      |
| West      | 848                 | 1048               | 0.8092      |